
% Approximation of knowledge production function

cd /Users/andreas/Dropbox/Work/PATSTAT/matlab

clear
close all
s=5;
k=8;
b=(1-s)/(k-s+1);
T0 = .2;
tauhat = @(T1) (1+T1)./(1+T0);
DeltaT = @(T1) T1-T0;


hold on;
b=-1;
lnKhat = @(T1) log(tauhat(T1).^b);
DeltalnK = @(T1)1/b.*DeltaT(T1);
fplot(lnKhat,[0 .2],"-")
fplot(DeltalnK,[0 .2],"-.")

legend({'True','Approximation'},'FontSize',12)
legend('boxoff')
xlabel('T_1','FontSize',12)
ylabel('\Delta lnK','FontSize',12)
saveas(gcf,'approximation2019.pdf');
saveas(gcf,'approximation2019.eps');
